Nicht aus der Schweiz? Besuchen Sie lehmanns.de

Polytopes, Rings, and K-Theory

Buch | Hardcover
461 Seiten
2009
Springer-Verlag New York Inc.
978-0-387-76355-2 (ISBN)

Lese- und Medienproben

Polytopes, Rings, and K-Theory - Winfried Bruns, Joseph Gubeladze
CHF 299,55 inkl. MwSt
This book examines interactions of polyhedral discrete geometry and algebra. What makes this book unique is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory.
For every mathematician, ring theory and K-theory are intimately connected: al- braic K-theory is largely the K-theory of rings. At ?rst sight, polytopes, by their very nature, must appear alien to surveyors of this heartland of algebra. But in the presence of a discrete structure, polytopes de?ne a?ne monoids, and, in their turn, a?ne monoids give rise to monoid algebras. Teir spectra are the building blocks of toric varieties, an area that has developed rapidly in the last four decades. From a purely systematic viewpoint, "monoids" should therefore replace "po- topes" in the title of the book. However, such a change would conceal the geometric ?avor that we have tried to preserve through all chapters. Before delving into a description of the contents we would like to mention three general features of the book: (?) the exhibiting of interactions of convex geometry, ring theory, and K-theory is not the only goal; we present some of the central results in each of these ?elds; (?) the exposition is of constructive (i. e., algorithmic) nature at many places throughout the text-there is no doubt that one of the driving forces behind the current popularity of combinatorial geometry is the quest for visualization and computation; (?
) despite the large amount of information from various ?elds, we have strived to keep the polytopal perspective as the major organizational principle.

I Cones, monoids, and triangulations.- Polytopes, cones, and complexes.- Affine monoids and their Hilbert bases.- Multiples of lattice polytopes.- II Affine monoid algebras.- Monoid algebras.- Isomorphisms and automorphisms.- Homological properties and Hilbert functions.- Gr#x00F6;bner bases, triangulations, and Koszul algebras.- III K-theory.- Projective modules over monoid rings.- Bass#x2013;Whitehead groups of monoid rings.- Varieties.

Erscheint lt. Verlag 27.5.2009
Reihe/Serie Springer Monographs in Mathematics
Zusatzinfo 52 Illustrations, black and white; XIV, 461 p. 52 illus.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 0-387-76355-4 / 0387763554
ISBN-13 978-0-387-76355-2 / 9780387763552
Zustand Neuware
Informationen gemäß Produktsicherheitsverordnung (GPSR)
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich
Begriffe, Sätze und zahlreiche Beispiele in kurzen Lerneinheiten

von Christian Karpfinger

Buch | Softcover (2022)
Springer Spektrum (Verlag)
CHF 76,95